Question

We predict that learning statistics will increase a student's IQ. Those not learning statistics have a population mean of 100 with a standard deviation of 15. For 25 statistics students, the mean is equal to 108.6. Use a Z test and the 10 step processto determine if learning statistics increases a student's IQ.

Step 1: Research Hypothesis?

Step 2: Null Hypothesis?

Step 3: One or two tails?

Step 4: Alpha level?

Step 5: What test?

Step 6: Degrees of Freedom?N/A

Step 7: Critical Value?

Step 8: Decision Rule?

Step 9: Finding?

Step 10: Conclusion?

Answer 1

The solution to this problem is given below

variance as x. lot X be a mandam variable measuring the TQ of the stualants not horning Statisties. Griven X~ N(100, 15²). Let y be another mandam variable measuring asuring th the IQ of the students learning statistics. We assume that y has the same . Y~ N(M, 15²), whore M is unknown. ado Let X, X2 Xes be a random sample on X and You Y... Yes be a random sample on Y. Let à and Y be the corresponding sample means. XnN (100, 1), TNN (u. 18) Here we want to test, Hoil= 100 against HiM 2100 Thus it is a one-tailed test. We take st level ob Got sine ficance here. Here the test statistic is under Ho, Z - Qard (7-100525 18

V25 We woject Ho at St. level of significance if z > Zaos sie X > 100+ 15 Zoos where Zoos ca obtained from the standard normal table. Now, is given as 108.6. zam (108.6 - 10925 15 X = 2:867 From the standard normal table, Zo.es = 1.64 ! a Since Zobs = 2.867 > 1.64, we poject Ho at st level of significance This eve cor can conclude that Statistics a to increases learning student's TQ. lead